Algorithms for Constrained Best-fit Alignment

Laure Brisoux Devendeville (1) , Serge Dumont (2) , Olivier Goubet (2) , Sylvain Lefebvre (3)

1 MIS - Modélisation, Information et Systèmes - UR UPJV 4290
2 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée
3 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée - UMR CNRS 7352

Manufacturing complex structures as planes requires the assembly of several pieces. The first step in the process is to align the pieces. This article is concerned with some mathematical and computational aspects of new algorithms devoted to the alignment of the pieces. We describe the properties of suitable algorithms to handle a non standard constrained optimization problem that occurs in the assembly process of a manufactured product. Then we present two kinds of algorithms: the first based on a fractional step algorithm and the second on a local search algorithm. We assess them on real cases and compare their results with an evolutionary algorithm for difficult non-linear or non-convex optimization problems in continuous domain.

Domaines: Mathématique discrète [cs.DM]; Analyse numérique [cs.NA]; Recherche opérationnelle [math.OC]

Laure Brisoux Devendeville, Serge Dumont, Olivier Goubet, Sylvain Lefebvre. Algorithms for Constrained Best-fit Alignment. Journal of Informatics and Mathematical Sciences, 2013, 5 (2), pp.77-100. ⟨10.26713/jims.v5i2.180⟩. ⟨hal-00999255⟩